I'm in a music appreciation class. I have to write a paper describing the various elements of two songs. By the time I get a reply, it will be too late, but I still really want to learn this as well as I can.
What are some words that could be used to describe the melody of a song?
Notes in a melody are often described by the intervals between them, using a movement-based metaphor. An interval can be a "step" (neighboring notes in a scale--which are sometimes considered to be steps on a ladder) or a "leap," when the interval is larger than a single step.
Continuing with the movement metaphor, if the leap is downward in pitch, it is called a "falling" interval. If it is upward in pitch, it is a "rising interval".
Sometimes it is fair game to take this further if the melody has particular or striking movement characteristics, e.g., a gentle rocking motion, like a lullaby, or a more jagged or thrusting shape (think "Ride of the Valkyries") or a more circuitous or wandering shape (e.g., the pastoral English Horn solo in William Tell Overture), or 'sighing' like the first melody in Schubert's 'Unfinished'.
As you get more technical, harmonic characteristics (scale, chord) and rhythmic characteristics (strong beats/weak beats, passing tones, syncopation) as well as motif, phrase and sentence structure are discussed.
To amplify on Phil and Laurence's answers, many musicologists and others studying music describe melodies as being either "scale driven" or "harmony driven." I'm betting that's what this class is fishing for you to come up with. A scale-driven melody is one that moves mostly by step and/or half-step and follows a certain type of scale most of the time. A harmony-driven melody is one that moves mostly by arpeggiating through the notes of various chords.
If you're into classical at all, a good example of harmony-driven would be the opening theme of Beethoven's 3rd symphony. A good example of scale-driven would be the initial melody in the slow movement of Rachmaninoff's 2nd Symphony. There are many other examples, whether in classical or other genres.
I agree with @ToddWilcox comment. If this is a technical question then you need a more technical answer. Something like what @PhilFreihofner says but possibly with more detail about some of the actual intervals used. From what you say someone should be able to get a reasonable idea of what the music was like although, unless you sang it to them, they would not know exactly how it sounded.
If you are in a non-technical class then the starting point is your emotional reaction to what you are hearing. What does it make you think of, how does it make you feel and, if possible, why do you react like that? In this case there are no "right" or "wrong" answers because you are giving a personal account.
Also bear in mind that you were asked to describe elements of the songs, not just the tunes, so you need to describe the accompaniments and arrangements as well as the melodies.
I expect they want you to talk about how the melody is constructed from bits of scale, bits of arpeggio, repeated patterns, both melodic and rhythmic, with or without modification ('sequence' is a good word)... That sort of thing.
There are many, many other terms and aspects of melody to consider. But the list above provides some melody specific terms that can be used to objectively describe a melody.
